Carbon burning powers scenarios that influence the fate of stars, such as the late evolutionary stages of massive stars (exceeding eight solar masses) and superbursts from accreting neutron stars. It proceeds through the C +C fusion reactions that produce an alpha particle and neon-20 or a proton and sodium-23-that is, C(C, α)Ne and C(C, p)Na-at temperatures greater than 0.4 × 10 kelvin, corresponding to astrophysical energies exceeding a megaelectronvolt, at which such nuclear reactions are more likely to occur in stars. The cross-sections for those carbon fusion reactions (probabilities that are required to calculate the rate of the reactions) have hitherto not been measured at the Gamow peaks below 2 megaelectronvolts because of exponential suppression arising from the Coulomb barrier. The reference rate at temperatures below 1.2 × 10 kelvin relies on extrapolations that ignore the effects of possible low-lying resonances. Here we report the measurement of the C(C, α)Ne and C(C, p)Na reaction rates (where the subscripts 0 and 1 stand for the ground and first excited states of Ne andNa, respectively) at centre-of-mass energies from 2.7 to 0.8 megaelectronvolts using the Trojan Horse method and the deuteron in N. The cross-sections deduced exhibit several resonances that are responsible for very large increases of the reaction rate at relevant temperatures. In particular, around 5 × 10 kelvin, the reaction rate is boosted to more than 25 times larger than the reference value . This finding may have implications such as lowering the temperatures and densities required for the ignition of carbon burning in massive stars and decreasing the superburst ignition depth in accreting neutron stars to reconcile observations with theoretical models .

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The14 C(n, γ) 15 C reaction plays an important role in inhomogeneous big bang models. In [N. K. Timofeyuk et al., Phys. Rev. Lett. 96, 162501 (2006)] it was shown that the 14 C(n, γ) 15 C radiative capture at astrophysically relevant energies is peripheral reaction, i.e. the overall normalization of its cross section is determined by the asymptotic normalization coefficient (ANC) for 15 C → 14 C+n. Here we present new measurements of the 14 C(d, p) 15 C differential cross sections at deuteron incident energy of 17.06 MeV and the analysis to determine the ANCs for neutron removal from the ground and first excited states of 15 C. The results are compared with the previous estimations.